Examples of dual clutch transmissions are described in U.S. patents and patent applications U.S. Pat. Nos. 5,711,409; 6,996,989; 6,887,184; 6,909,955; 2006/0101933A1; and 2006/0207655A1. It is desirable to provide a dual clutch transmission arrangement that incorporates a positive pressure lubrication cooler heat exchanger integrated into a wet clutch module cover of the transmission. It is desirable to provide a dual clutch transmission with a cover as mentioned above wherein the lubricant is delivered adjacent a bearing which allows the cover to support a main input shaft of the transmission.